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- Random vs. Systematic Error | Definition & Examples
Random vs. Systematic Error | Definition & Examples
Published on May 7, 2021 by Pritha Bhandari . Revised on June 22, 2023.
In scientific research, measurement error is the difference between an observed value and the true value of something. It’s also called observation error or experimental error.
There are two main types of measurement error:
Random error is a chance difference between the observed and true values of something (e.g., a researcher misreading a weighing scale records an incorrect measurement).
- Systematic error is a consistent or proportional difference between the observed and true values of something (e.g., a miscalibrated scale consistently registers weights as higher than they actually are).
By recognizing the sources of error, you can reduce their impacts and record accurate and precise measurements. Gone unnoticed, these errors can lead to research biases like omitted variable bias or information bias .
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Are random or systematic errors worse, random error, reducing random error, systematic error, reducing systematic error, other interesting articles, frequently asked questions about random and systematic error.
In research, systematic errors are generally a bigger problem than random errors.
Random error isn’t necessarily a mistake, but rather a natural part of measurement. There is always some variability in measurements, even when you measure the same thing repeatedly, because of fluctuations in the environment, the instrument, or your own interpretations.
But variability can be a problem when it affects your ability to draw valid conclusions about relationships between variables . This is more likely to occur as a result of systematic error.
Precision vs accuracy
Random error mainly affects precision , which is how reproducible the same measurement is under equivalent circumstances. In contrast, systematic error affects the accuracy of a measurement, or how close the observed value is to the true value.
Taking measurements is similar to hitting a central target on a dartboard. For accurate measurements, you aim to get your dart (your observations) as close to the target (the true values) as you possibly can. For precise measurements, you aim to get repeated observations as close to each other as possible.
Random error introduces variability between different measurements of the same thing, while systematic error skews your measurement away from the true value in a specific direction.
When you only have random error, if you measure the same thing multiple times, your measurements will tend to cluster or vary around the true value. Some values will be higher than the true score, while others will be lower. When you average out these measurements, you’ll get very close to the true score.
For this reason, random error isn’t considered a big problem when you’re collecting data from a large sample—the errors in different directions will cancel each other out when you calculate descriptive statistics . But it could affect the precision of your dataset when you have a small sample.
Systematic errors are much more problematic than random errors because they can skew your data to lead you to false conclusions. If you have systematic error, your measurements will be biased away from the true values. Ultimately, you might make a false positive or a false negative conclusion (a Type I or II error ) about the relationship between the variables you’re studying.
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Random error affects your measurements in unpredictable ways: your measurements are equally likely to be higher or lower than the true values.
In the graph below, the black line represents a perfect match between the true scores and observed scores of a scale. In an ideal world, all of your data would fall on exactly that line. The green dots represent the actual observed scores for each measurement with random error added.
Random error is referred to as “noise”, because it blurs the true value (or the “signal”) of what’s being measured. Keeping random error low helps you collect precise data.
Sources of random errors
Some common sources of random error include:
- natural variations in real world or experimental contexts.
- imprecise or unreliable measurement instruments.
- individual differences between participants or units.
- poorly controlled experimental procedures.
Random error source | Example |
---|---|
Natural variations in context | In an about memory capacity, your participants are scheduled for memory tests at different times of day. However, some participants tend to perform better in the morning while others perform better later in the day, so your measurements do not reflect the true extent of memory capacity for each individual. |
Imprecise instrument | You measure wrist circumference using a tape measure. But your tape measure is only accurate to the nearest half-centimeter, so you round each measurement up or down when you record data. |
Individual differences | You ask participants to administer a safe electric shock to themselves and rate their pain level on a 7-point rating scale. Because pain is subjective, it’s hard to reliably measure. Some participants overstate their levels of pain, while others understate their levels of pain. |
Random error is almost always present in research, even in highly controlled settings. While you can’t eradicate it completely, you can reduce random error using the following methods.
Take repeated measurements
A simple way to increase precision is by taking repeated measurements and using their average. For example, you might measure the wrist circumference of a participant three times and get slightly different lengths each time. Taking the mean of the three measurements, instead of using just one, brings you much closer to the true value.
Increase your sample size
Large samples have less random error than small samples. That’s because the errors in different directions cancel each other out more efficiently when you have more data points. Collecting data from a large sample increases precision and statistical power .
Control variables
In controlled experiments , you should carefully control any extraneous variables that could impact your measurements. These should be controlled for all participants so that you remove key sources of random error across the board.
Systematic error means that your measurements of the same thing will vary in predictable ways: every measurement will differ from the true measurement in the same direction, and even by the same amount in some cases.
Systematic error is also referred to as bias because your data is skewed in standardized ways that hide the true values. This may lead to inaccurate conclusions.
Types of systematic errors
Offset errors and scale factor errors are two quantifiable types of systematic error.
An offset error occurs when a scale isn’t calibrated to a correct zero point. It’s also called an additive error or a zero-setting error.
A scale factor error is when measurements consistently differ from the true value proportionally (e.g., by 10%). It’s also referred to as a correlational systematic error or a multiplier error.
You can plot offset errors and scale factor errors in graphs to identify their differences. In the graphs below, the black line shows when your observed value is the exact true value, and there is no random error.
The blue line is an offset error: it shifts all of your observed values upwards or downwards by a fixed amount (here, it’s one additional unit).
The purple line is a scale factor error: all of your observed values are multiplied by a factor—all values are shifted in the same direction by the same proportion, but by different absolute amounts.
Sources of systematic errors
The sources of systematic error can range from your research materials to your data collection procedures and to your analysis techniques. This isn’t an exhaustive list of systematic error sources, because they can come from all aspects of research.
Response bias occurs when your research materials (e.g., questionnaires ) prompt participants to answer or act in inauthentic ways through leading questions . For example, social desirability bias can lead participants try to conform to societal norms, even if that’s not how they truly feel.
Your question states: “Experts believe that only systematic actions can reduce the effects of climate change. Do you agree that individual actions are pointless?”
Experimenter drift occurs when observers become fatigued, bored, or less motivated after long periods of data collection or coding, and they slowly depart from using standardized procedures in identifiable ways.
Initially, you code all subtle and obvious behaviors that fit your criteria as cooperative. But after spending days on this task, you only code extremely obviously helpful actions as cooperative.
Sampling bias occurs when some members of a population are more likely to be included in your study than others. It reduces the generalizability of your findings, because your sample isn’t representative of the whole population.
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You can reduce systematic errors by implementing these methods in your study.
Triangulation
Triangulation means using multiple techniques to record observations so that you’re not relying on only one instrument or method.
For example, if you’re measuring stress levels, you can use survey responses, physiological recordings, and reaction times as indicators. You can check whether all three of these measurements converge or overlap to make sure that your results don’t depend on the exact instrument used.
Regular calibration
Calibrating an instrument means comparing what the instrument records with the true value of a known, standard quantity. Regularly calibrating your instrument with an accurate reference helps reduce the likelihood of systematic errors affecting your study.
You can also calibrate observers or researchers in terms of how they code or record data. Use standard protocols and routine checks to avoid experimenter drift.
Randomization
Probability sampling methods help ensure that your sample doesn’t systematically differ from the population.
In addition, if you’re doing an experiment, use random assignment to place participants into different treatment conditions. This helps counter bias by balancing participant characteristics across groups.
Wherever possible, you should hide the condition assignment from participants and researchers through masking (blinding) .
Participants’ behaviors or responses can be influenced by experimenter expectancies and demand characteristics in the environment, so controlling these will help you reduce systematic bias.
If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.
- Normal distribution
- Degrees of freedom
- Null hypothesis
- Discourse analysis
- Control groups
- Mixed methods research
- Non-probability sampling
- Quantitative research
- Ecological validity
Research bias
- Rosenthal effect
- Implicit bias
- Cognitive bias
- Selection bias
- Negativity bias
- Status quo bias
Random and systematic error are two types of measurement error.
Systematic error is a consistent or proportional difference between the observed and true values of something (e.g., a miscalibrated scale consistently records weights as higher than they actually are).
Systematic error is generally a bigger problem in research.
With random error, multiple measurements will tend to cluster around the true value. When you’re collecting data from a large sample , the errors in different directions will cancel each other out.
Systematic errors are much more problematic because they can skew your data away from the true value. This can lead you to false conclusions ( Type I and II errors ) about the relationship between the variables you’re studying.
Random error is almost always present in scientific studies, even in highly controlled settings. While you can’t eradicate it completely, you can reduce random error by taking repeated measurements, using a large sample, and controlling extraneous variables .
You can avoid systematic error through careful design of your sampling , data collection , and analysis procedures. For example, use triangulation to measure your variables using multiple methods; regularly calibrate instruments or procedures; use random sampling and random assignment ; and apply masking (blinding) where possible.
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The Scientific Method/Control of Measurement Errors
Experimental design.
Perhaps the most important step in controlling experimental error is to design your experiments to produce as little systematic error as possible. In order to do this, it is important to know something about what you are measuring. As an example, suppose that you desired to measure the weight of the oxygen produced in the decomposition of hydrogen peroxide:
You would need to ask yourself: How would you separate the oxygen from the water and unreacted hydrogen peroxide? How will you prevent the oxygen from leaking? Do you want to measure the weight directly, or by calculating it from other values (such as pressure)?
Get into the habit of asking yourself, "what could go wrong with this experiment?" before you start the experiment. Then if you can, design it so that the things that could go wrong are as minor as possible, and then when performing it be as careful as possible to avoid what is left.
Calibration and Accuracy
All measurement instruments need to be calibrated in some way in order to ensure that the values that are read are near the true value of the property being measured. Rulers all are compared to a standard when they are made so that when an inch is marked on the ruler, it is truly an inch.
Many instruments lose their calibration, and hence their accuracy, over time. Therefore it is necessary to recalibrate them. Instruments are generally re-calibrated by measurement of a standard or several, which have well-defined properties. For example, a scale might be calibrated by weighing a 5g weight and adjusting a dial until the reading is 5.000 g. Follow the instrument manual closely for calibration procedures, so that any bias in measurement due to measurement inaccuracy can be mitigated.
Repeatability and Precision
Measurement instruments never will give you an exact answer. For example, if you are measuring the volume of a liquid in a graduated cylinder, it is necessary for you to estimate which of the hash marks on the instrument is the closest to the true volume (or to interpolate between them based on your eyesight). Most computerized measurement devices, such as many modern scales, take multiple measurements and average them to obtain accurate results, but these also have sensitivity limitations.
Manufacturers often report the precision of their instruments. The repeatability of an instrument is a measure of the precision, which is the similarity of successive measurements of an identical quantity to each other. Reproducibility is essentially the ability to, with all other conditions the same (or as close to the same as possible), achieve the same measurement value in an experiment. For example, you may measure the weight of an object with the same scale multiple times. If the reading is significantly different every time, it is possible that the instrument needs to be recalibrated or re-stabilized (for example, by cleaning out dust from the receiver, or making sure the setup is right). If it has been properly calibrated and set up and measurements still vary more than the precision claimed by the manufacturer, the instrument may be broken.
Reproducibility
Another way to control errors in measurement from experiment to experiment is to constantly assess the reproducibility of the measurements. Reproducibility is measured essentially by performing the same measurement multiple times while varying one part of the experiment. For example, if you are measuring the pH of a buffer as part of a process, you may assess the reproducibility of the buffer preparation by preparing the same sample several times, independently of each other, and measuring the pH of each sample. If the variance in the pH measurements is larger than the measurement accuracy (or repeatability ) of the instrument, then it is likely that the preparation of the buffer is to blame for this error. Such tests can be performed on many parts of a larger process in order to pinpoint and remedy the largest control difficulties.
Another possible reproducibility test would be measuring the same sample with different pH meters. It is very important to test the compatibility of different measurement instruments before claiming that the results are comparable, and such reproducibility measurements are critical for determining the relationship between two instruments.
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Sources of Error in Science Experiments
Science labs usually ask you to compare your results against theoretical or known values. This helps you evaluate your results and compare them against other people’s values. The difference between your results and the expected or theoretical results is called error. The amount of error that is acceptable depends on the experiment, but a margin of error of 10% is generally considered acceptable. If there is a large margin of error, you’ll be asked to go over your procedure and identify any mistakes you may have made or places where error might have been introduced. So, you need to know the different types and sources of error and how to calculate them.
How to Calculate Absolute Error
One method of measuring error is by calculating absolute error , which is also called absolute uncertainty. This measure of accuracy is reported using the units of measurement. Absolute error is simply the difference between the measured value and either the true value or the average value of the data.
absolute error = measured value – true value
For example, if you measure gravity to be 9.6 m/s 2 and the true value is 9.8 m/s 2 , then the absolute error of the measurement is 0.2 m/s 2 . You could report the error with a sign, so the absolute error in this example could be -0.2 m/s 2 .
If you measure the length of a sample three times and get 1.1 cm, 1.5 cm, and 1.3 cm, then the absolute error is +/- 0.2 cm or you would say the length of the sample is 1.3 cm (the average) +/- 0.2 cm.
Some people consider absolute error to be a measure of how accurate your measuring instrument is. If you are using a ruler that reports length to the nearest millimeter, you might say the absolute error of any measurement taken with that ruler is to the nearest 1 mm or (if you feel confident you can see between one mark and the next) to the nearest 0.5 mm.
How to Calculate Relative Error
Relative error is based on the absolute error value. It compares how large the error is to the magnitude of the measurement. So, an error of 0.1 kg might be insignificant when weighing a person, but pretty terrible when weighing a apple. Relative error is a fraction, decimal value, or percent.
Relative Error = Absolute Error / Total Value
For example, if your speedometer says you are going 55 mph, when you’re really going 58 mph, the absolute error is 3 mph / 58 mph or 0.05, which you could multiple by 100% to give 5%. Relative error may be reported with a sign. In this case, the speedometer is off by -5% because the recorded value is lower than the true value.
Because the absolute error definition is ambiguous, most lab reports ask for percent error or percent difference.
How to Calculate Percent Error
The most common error calculation is percent error , which is used when comparing your results against a known, theoretical, or accepted value. As you probably guess from the name, percent error is expressed as a percentage. It is the absolute (no negative sign) difference between your value and the accepted value, divided by the accepted value, multiplied by 100% to give the percent:
% error = [accepted – experimental ] / accepted x 100%
How to Calculate Percent Difference
Another common error calculation is called percent difference . It is used when you are comparing one experimental result to another. In this case, no result is necessarily better than another, so the percent difference is the absolute value (no negative sign) of the difference between the values, divided by the average of the two numbers, multiplied by 100% to give a percentage:
% difference = [experimental value – other value] / average x 100%
Sources and Types of Error
Every experimental measurement, no matter how carefully you take it, contains some amount of uncertainty or error. You are measuring against a standard, using an instrument that can never perfectly duplicate the standard, plus you’re human, so you might introduce errors based on your technique. The three main categories of errors are systematic errors, random errors , and personal errors. Here’s what these types of errors are and common examples.
Systematic Errors
Systematic error affects all the measurements you take. All of these errors will be in the same direction (greater than or less than the true value) and you can’t compensate for them by taking additional data. Examples of Systematic Errors
- If you forget to calibrate a balance or you’re off a bit in the calibration, all mass measurements will be high/low by the same amount. Some instruments require periodic calibration throughout the course of an experiment , so it’s good to make a note in your lab notebook to see whether the calibrations appears to have affected the data.
- Another example is measuring volume by reading a meniscus (parallax). You likely read a meniscus exactly the same way each time, but it’s never perfectly correct. Another person taking the reading may take the same reading, but view the meniscus from a different angle, thus getting a different result. Parallax can occur in other types of optical measurements, such as those taken with a microscope or telescope.
- Instrument drift is a common source of error when using electronic instruments. As the instruments warm up, the measurements may change. Other common systematic errors include hysteresis or lag time, either relating to instrument response to a change in conditions or relating to fluctuations in an instrument that hasn’t reached equilibrium. Note some of these systematic errors are progressive, so data becomes better (or worse) over time, so it’s hard to compare data points taken at the beginning of an experiment with those taken at the end. This is why it’s a good idea to record data sequentially, so you can spot gradual trends if they occur. This is also why it’s good to take data starting with different specimens each time (if applicable), rather than always following the same sequence.
- Not accounting for a variable that turns out to be important is usually a systematic error, although it could be a random error or a confounding variable. If you find an influencing factor, it’s worth noting in a report and may lead to further experimentation after isolating and controlling this variable.
Random Errors
Random errors are due to fluctuations in the experimental or measurement conditions. Usually these errors are small. Taking more data tends to reduce the effect of random errors. Examples of Random Errors
- If your experiment requires stable conditions, but a large group of people stomp through the room during one data set, random error will be introduced. Drafts, temperature changes, light/dark differences, and electrical or magnetic noise are all examples of environmental factors that can introduce random errors.
- Physical errors may also occur, since a sample is never completely homogeneous. For this reason, it’s best to test using different locations of a sample or take multiple measurements to reduce the amount of error.
- Instrument resolution is also considered a type of random error because the measurement is equally likely higher or lower than the true value. An example of a resolution error is taking volume measurements with a beaker as opposed to a graduated cylinder. The beaker will have a greater amount of error than the cylinder.
- Incomplete definition can be a systematic or random error, depending on the circumstances. What incomplete definition means is that it can be hard for two people to define the point at which the measurement is complete. For example, if you’re measuring length with an elastic string, you’ll need to decide with your peers when the string is tight enough without stretching it. During a titration, if you’re looking for a color change, it can be hard to tell when it actually occurs.
Personal Errors
When writing a lab report, you shouldn’t cite “human error” as a source of error. Rather, you should attempt to identify a specific mistake or problem. One common personal error is going into an experiment with a bias about whether a hypothesis will be supported or rejects. Another common personal error is lack of experience with a piece of equipment, where your measurements may become more accurate and reliable after you know what you’re doing. Another type of personal error is a simple mistake, where you might have used an incorrect quantity of a chemical, timed an experiment inconsistently, or skipped a step in a protocol.
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Understanding Experimental Errors: Types, Causes, and Solutions
Types of experimental errors.
In scientific experiments, errors can occur that affect the accuracy and reliability of the results. These errors are often classified into three main categories: systematic errors, random errors, and human errors. Here are some common types of experimental errors:
1. Systematic Errors
Systematic errors are consistent and predictable errors that occur throughout an experiment. They can arise from flaws in equipment, calibration issues, or flawed experimental design. Some examples of systematic errors include:
– Instrumental Errors: These errors occur due to inaccuracies or limitations of the measuring instruments used in the experiment. For example, a thermometer may consistently read temperatures slightly higher or lower than the actual value.
– Environmental Errors: Changes in environmental conditions, such as temperature or humidity, can introduce systematic errors. For instance, if an experiment requires precise temperature control, fluctuations in the room temperature can impact the results.
– Procedural Errors: Errors in following the experimental procedure can lead to systematic errors. This can include improper mixing of reagents, incorrect timing, or using the wrong formula or equation.
2. Random Errors
Random errors are unpredictable variations that occur during an experiment. They can arise from factors such as inherent limitations of measurement tools, natural fluctuations in data, or human variability. Random errors can occur independently in each measurement and can cause data points to scatter around the true value. Some examples of random errors include:
– Instrument Noise: Instruments may introduce random noise into the measurements, resulting in small variations in the recorded data.
– Biological Variability: In experiments involving living organisms, natural biological variability can contribute to random errors. For example, in studies involving human subjects, individual differences in response to a treatment can introduce variability.
– Reading Errors: When taking measurements, human observers can introduce random errors due to imprecise readings or misinterpretation of data.
3. Human Errors
Human errors are mistakes or inaccuracies that occur due to human factors, such as lack of attention, improper technique, or inadequate training. These errors can significantly impact the experimental results. Some examples of human errors include:
– Data Entry Errors: Mistakes made when recording data or entering data into a computer can introduce errors. These errors can occur due to typographical mistakes, transposition errors, or misinterpretation of results.
– Calculation Errors: Errors in mathematical calculations can occur during data analysis or when performing calculations required for the experiment. These errors can result from mathematical mistakes, incorrect formulas, or rounding errors.
– Experimental Bias: Personal biases or preconceived notions held by the experimenter can introduce bias into the experiment, leading to inaccurate results.
It is crucial for scientists to be aware of these types of errors and take measures to minimize their impact on experimental outcomes. This includes careful experimental design, proper calibration of instruments, multiple repetitions of measurements, and thorough documentation of procedures and observations.
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COMMENTS
Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measurements of a constant attribute or quantity are taken. Systematic errors are errors that are not determined by chance but are introduced by repeatable processes inherent to the system. [3]
For example, an experimental uncertainty analysis of an undergraduate physics lab experiment in which a pendulum can estimate the value of the local gravitational acceleration constant g.The relevant equation [1] for an idealized simple pendulum is, approximately, = [+ ()] where T is the period of oscillation (seconds), L is the length (meters), and θ is the initial angle.
Famous experimental errors. A reported faint visual effect that experimenters could still "see" even when the supposed causative element in their apparatus had been secretly disconnected. [6] Published in Annalen der Physik and said to be the first journal paper to cite Einstein's 1905 electrodynamics paper.
Random and systematic errors are types of measurement error, a difference between the observed and true values of something.
1Adapted from "Introduction to Experimental Error," Susan Cartwright, University of Sheffield, UK (2003). 2This is referred to as the mode. 1. 2 APPENDIX A. MEASUREMENT AND ERROR ANALYSIS The student also decides to calculate the average (or mean) head count n¯ for the 100 trials, knowing
Learn about absolute and relative error. See their formulas and get examples of how to calculate them in science.
The repeatability of an instrument is a measure of the precision, which is the similarity of successive measurements of an identical quantity to each other. Reproducibility is essentially the ability to, with all other conditions the same (or as close to the same as possible), achieve the same measurement value in an experiment. For example ...
Random errors are due to fluctuations in the experimental or measurement conditions. Usually these errors are small. Taking more data tends to reduce the effect of random errors. Examples of Random Errors
from experimental data. In this lab course, we will be using Microsoft Excel to record ... Systematic errors are usually due to imperfections in the equipment, improper or biased observation, or the presence of additional physical e ects not taken into account. (An example might be an experiment on forces and acceleration in which
In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, ... When the variables are the values of experimental measurements they have uncertainties due to measurement limitations (e.g., instrument precision) which propagate due to the combination of variables in the function.
These errors are often classified into three main categories: systematic errors, random errors, and human errors. Here are some common types of experimental errors: 1. Systematic Errors. Systematic errors are consistent and predictable errors that occur throughout an experiment. They can arise from flaws in equipment, calibration issues, or ...
This chapter is largely a tutorial on handling experimental errors of measurement. Much of the material has been extensively tested with science undergraduates at a variety of levels at the University of Toronto. Whole books can and have been written on this topic but here we distill the topic down to the essentials. Nonetheless, our experience ...
Random Errors, Systematic Errors, and Mistakes There are three basic categories of experimental issues that students often think of under the heading of experimental error, or uncertainty.
Language links are at the top of the page across from the title.
pressing experimental uncertainty to be discussed in the next chapter and developed throughout this book. Sources of Errors The three principal kinds of errors in experimental measurements are sys tematic errors, random errors, and blunders. The first two kinds are pres ent in all measurements of a continuous variable, and the last should be
Design of experiments. The design of experiments (DOE or DOX), also known as experiment design or experimental design, is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associated with experiments in which the design ...
Experimental Error: Achieving Immortality. Robert Bunsen was a renowned chemist, the kind of serious 19th century German academic whose photograph makes you glad you didn't attend graduate school in an era of three-piece suits and puffy neck beards. During his illustrious career, he found an antidote for arsenic poisoning, co-discovered two ...
©2006 Six Sigma eLearning, Inc. 1.800.297.8230 Six Sigma eLearning, Inc. 1.800.297.8230
In the scientific method, an experiment is an empirical procedure that arbitrates competing models or hypotheses. [2] [3] Researchers also use experimentation to test existing theories or new hypotheses to support or disprove them.[3] [4]An experiment usually tests a hypothesis, which is an expectation about how a particular process or phenomenon works.. However, an experiment may also aim to ...